A last-gasp own-goal broke Paderborn hearts as they slumped to a 1-0 defeat at Schalke.
Wolfsburg regained second spot from Borussia Monchengladbach and left Paderborn inside the bottom two with a 3-1 win.
Bas Dost scored twice as Wolfsburg secured a Champions League spot, while Cologne guaranteed survival.
Paderborn came from behind to move out of the relegation zone and above their hosts Freiburg with a 2-1 win
Paderborn threw away a two-goal lead in their 2-2 Bundesliga draw against Werder Bremen.
Borussia Dortmund's first game after Jurgen Klopp announced his summer exit ended in a 3-0 win over Paderborn.